3. Shear transformation
Exp. Martensite can be generated by shear on γ
Both shears are possible
and identical to Bain
distortion if disregarded
the rigid body rotation. 3
4. Shear transformation
Shear of cooperative movements of atoms can
be in different planes rather than (111)γ plane,
depending on alloy composition and
transformation temp.
Shear does not have to act along the same
direction on every parallel atomic plane.
4
5. Shear transformation
Greninger and Troiano (1949) found that
Observed shear plane in Fe-22% Ni-0.8% C
was not the {111}γ plane and the shear angle
was 10.45°, not 19.5° as predicted by shear
mechanism.
Theysuggested that another shear had to be
added in order to complete the mechanism.
5
6. Double shear transformation
The first shear isa macroscopic shear
that contributes the shape change and
change in crystal structure.
The second shear is a microscopic shear.
Invariant plane
Bain distortion has no invariant plane
Lattice-invariant shear with Bain distortion
6
7. Invariant plane
During the martensitic transformation
The interface should be an invariant plane
Undistorted and unrotated plane
Any deformation on the invariant plane will
be termed an invariant plane strain.
7
8. From the Bain distortion
α lattice with bcc can be generated from
an fcc γ lattice by
Compression about 20% along
one principle axis and
a simultaneous uniform
expansion about 12% along
the other two axes perpendicular to
the first principle axis
8
9. Bain distortion of a sphere
Due to the Bain distortion
A unit sphere of the parent crystal
transforms into an oblate spheroid of the
product crystal
Contraction about 20% along the one
principle axis
Expansion about 12% along the other
two axes perpendicular to the first
principle axis
9
11. Bain distortion of a sphere
Due to the lattice deformation x12 + x2 + x3 = 1
2 2
Vectors OA’ and OB’
represent the final
position of vectors
Vectors OA and OB
represent the initial
position of the same
vectors
unchanged in
( x1 ) + ( x2 ) + ( x3 ) = 1
' 2 ' 2 ' 2
( 1.12 ) ( 1.12 ) ( 11 )
2 2 2
magnitude 0.80
12. Bain distortion of a sphere
Vectors unchanged in magnitude during
the lattice deformation
Corresponding to the
cones AOB and COD and
the cones A’OB’ and C’OD’
These vectors are termed
unextended lines.
A homogeneous strain would
result in an undistorted plane
of contact between the initial sphere of
austenite and the ellipsoid of martensite.
12
13. Bain distortion of a sphere
Allother vectors not involved in the cones
A’OB’ and C’OD’ would be
changed in magnitude.
Bain distortion would result
in no undistorted plane.
Hence, there is no invariant plane.
Very difficult to obtain a coherent planar
interface between the parent and the product
crystals only by the Bain distortion. 13
14. Bain distortion of a sphere
Therefore,Bain distortion
has no invariant plane.
14
15. Lattice-invariant shear
Lattice-invariant shear
must be of such
magnitude so as to produce
an undistorted plane
when combined with
the Bain distortion.
Consider slip or twinning
Must not make any
change in crystal structure.
15
16. Lattice-invariant shear
Graphical analysis of a simple shear of
slip or twinning of a unit sphere
Shear on an equatorial
plane K1 as the shear plane
d as the shear direction
α as shear angle Slip
16
17. Lattice-invariant shear
As a result of shear on K1
Any vector in the plane AK B is
2
transformed into a vector in
the plane AK’2B, which is
unchanged with length
although rotated relatively
to its original position.
The plane AK B is the initial Slip
2
position of a plane AK’2B,
which remains undistorted as
a result of the shear. 17
18. Lattice-invariant shear
As a result ofshear on K1
The relative positions of
the planes AK2B and AK’2B
depend on the amount of
shear involved.
The shear plane itself
remains undistorted
after shear. Slip
Vectors that remain invariant in length
(unextended lines) to this shear operation
are define as potential habit planes. 18
19. Lattice-invariant shear
As a result ofshear on K1
The relative positions of
the planes AK2B and AK’2B
depend on the amount of
shear involved.
The shear plane itself
remains undistorted
after shear. Slip
Vectors that remain invariant in length
(unextended lines) to this shear operation
are define as potential habit planes. 19
20. Lattice-invariant shear
When initial sphere → ellipsoid
by lattice deformation using
Bain distortion is distorted by
simple shear into another ellipsoid
+
and the lattice is left invariant,
The simple shear is termed
a lattice-invariant shear.
shear
20
22. Stereographic representation
of the Bain distortion
Any vector lying on the initial
cone AOB with a semiapex
of φ moves radially onto the
final cone A’OB’ with a
semiapex of φ’.
Vectors in the cones of
unextended lines do not
change their length,
but only the angle ∆φ.
22
23. Stereographic representation
of the lattice-invariant shear
An unextended line C
moves to the final position
along the circumference
of the great circle
defined by d*
(dash line).
23
24. Stereographic representation
of the lattice-invariant shear
Vectors in K’2 plane do not
change their length due to
shear, and the line OC’ in
the plane represents the final
position of an unextended line.
Line OC in K2 plane
represents the
initial position
of OC’.
24
25. Requirement for habit plane
Both Bain distortion and lattice
invariant shear provide an undistorted
plane for the habit plane.
Additional requirement is that the habit
plane be unrotated.
A rigid body rotation must be able to
return the undistorted plane to its
original position before
transformation.
25
27. Bain distortion with slip #1
Vectors b and c are defined
by the intersections of the
initial Bain cone with K1 plane
1.Apply a complementary shear
Vectors b and c become b’ and c’ and still lie
in the K1 plane and remain unchanged in
both direction and magnitude.
They are invariant lines.
27
28. Bain distortion with slip #1
Vectors b and c are defined
by the intersections of the
initial Bain cone with K1 plane
2.Apply a Bain distortion
Vectors b’ and c’ become b’’ and c’’ lie on the
initial and final Bain cones, respectively,
without changing their magnitude.
28
29. Bain distortion with slip #1
Complementary shear
b and c to b’ and c’
Bain distortion
b’ and c’ to b’’ and c’’
Angle btw b and c ≠ angle btw b” and c”
Appropriate rotation cannot be applied to
return b” and c” to initial positions of b and c.
Plane defined by b and c cannot be an invariant
plane. 29
30. Bain distortion with slip #2
To obtainan invariant plane,
must have other extended lines
Ifassumed to know
the shear angle α,
vectors a and d obtained from the intersections
of the K2 plane change to a’ and d’ along the
great circles.
Bain distortion,
vectors a’ and d’ become a” and d”, respectively
30
31. Bain distortion with slip #2
Through the transformation of
the complementary shear and
the Bain distortion
Sequences of a→a’→a”
and sequences d→d’→d”
reveal no change in length
However, angle btw a & d ≠ angle btw a” & d”
Plane defined by a and d cannot be an invariant
plane. 31
32. Complete transformation
process
Possible invariant planes will
depend on the choice of
combination of b or c
with a or d such as
Vectors a and b
Vectors a and c
Vectors b and d
Vectors c and d
32
33. Complete transformation
process
If theinvariant plane is the
plane defined by vectors a & c
Angle btw a & c = angle btw a’’ & c’’
Let the axis required for rotation
be at point u
Determine the amount of rotation
stereographically by intersection
of a great circle bisecting a-a”
with another great circle bisecting c-c” 33
34. Complete transformation
process
Once a” and c” coincide simultaneously
with a and c, respectively
Angle btw a & c = angle btw a’’ & c’’
Therefore, orientation relationship btw γ plane
(defined by the vectors a and c) and α’ plane
(defined by the vectors a” and c”) can be
determined for a specific variant of the Bain
distortion (B), lattice invariant shear (P), and
rotation operation (R).
T = BPR
34
36. Bain distortion with twinning
Twinned martensite can take place by having
alternate regions in the parent phase undergo
the lattice deformation along different
contraction axes, which are initially at right
angles to each other.
In the first region, contraction occurs along
the x3 [ 001] f axis.
In the adjacent region, contraction direction
can be either x1 [100] f or x2 [ 010] f axis.
Two rigid body rotations are also involved in
the twinning analysis. 36
37. Nucleation and growth
It only takes about 10-5 to 10-7 seconds for a plate
of martensite to grow to its full size.
The nucleation during the martensitic
transformation is extremely difficult to study
experimentally.
Average number of martensite is as large as 104
nuclei/mm3
Number of martensite nuclei can be
increased by increasing ∆T prior to Ms.
It is too small in term of number of
nucleation sites for homogeneous nucleation.
37
38. Nucleation and growth
Less likely to occur by homogeneous nucleation
process, but heterogeneous.
Surfaces and grain boundaries are not
significantly contributing to nucleation.
Most likely types of defect that could produce
the observed density of martensite nuclei are
dislocations (> 105 dislocation/mm2).
C. Zener (1948): movement of partial dislocations
during twinning could generate a thin bcc region
of lattice from an fcc region.
38
39. Nucleation and growth
Dissociation of a dislocation
into 2 partials is favorable
→ lower strain energy.
r r r
To generate b1 = b2 + b3
bcc structure, a a a
[ 110] = [ 211] + 121
the requirements are that all 2 6 6
green atoms move (shear)
a
forward by 12 [ 211] and an
additional dilatation
to correct lattice spacings. 39
40. Nucleation and growth
Growth of lath martensite with dimension
a > b >> c growing on a {111}γ planes
Thickening mechanism would involve the
nucleation and glide of transformation
dislocations moving on discrete ledges
behind the growing front.
Due to large misfit between
bct and fcc lattice,
dislocations could be
self-nucleated at the
lath interface as the lath moves forward.
40
41. Nucleation and growth
In medium and high carbon steels,
Morphology of martensite turns to change
from a lath to a plate-like shape.
As carbon concentration decreases,
Decrease lath structure
Decrease martensitic temperature
Increase twinning
Increase retained austenite
Depending on compositions, the habit plane
changes from {111}γ → {225}γ → {259}γ
41
42. Effect of pressure to martensite
As pressure increases
In Fe unary system, the equilibrium
temperature decreases
In Fe-C binary system, the phase region
around γ phase shifts to the left and
downward.
Similar to adding austenite stabilizer
42
43. Effect of alloying element to
martensite
Each alloying element will effect the martensitic
transformation differently.
If initially Hγ = Hα
When adding C
The ē of C will decrease Hα and cause α to
be less stable.
∆H = Hγ – Hα > 0, stabilize the γ
When adding X
Increase Hα and ∆H < 0, stabilize the α
43
44. Effect of external stress to
martensite
As martensite prefers to nucleate and grow
along the dislocation
Expected that an externally applied shear
stress will assist and accelerate the
generation of dislocations and hence the
growth of martensite.
An external shear stress can aid martensite
nucleation if the external elastic strain
components play as a part of the Bain strain.
This can also help by raising the M
s
temperature. 44
45. Effect of external stress to
martensite
Once the plastic deformation occurs
There is an upper limit value of M that the
s
stress can be applied.
The limit temp. of M is called M (highest
s d
temperature that stress helps to form
martensite)
Too much plastic deformation will
suppress the transformation.
45
46. Effect of external stress to
martensite
If a tensile
stress is applied
M temperature can be suppressed to lower
s
temperature
Transformation may be reversed from α’ →
γ
Presence of large magnetic field may favor the
formation of the ferromagnetic phase and
therefore raise Ms temp.
46
47. Effect of external stress to
martensite
Plastic deformation of γ before transformation
will assist on increasing number of nucleation
sites.
Once the transformation occurs
Result in very fine plate size of martensite
(Called the ausforming process)
Combined effect of very fine martensite plates,
1
2
solution hardening of carbon, and 3dislocation
hardening
Very high strength ausformed steel 47
48. Shape-memory alloys (SMA)
Unique property of some alloys
After being deformed at one temperature,
they recover the original undeformed shape
when heated to a higher temperature.
48
49. Shape-memory alloys (SMA)
Unique property of some alloys
After being deformed at one temperature,
they recover the original undeformed shape
when heated to a higher temperature.
Fundamental to the shape-memory effect
(SME) is the occurrence of a martensitic phase
transformation and its subsequent reversal.
Alloys: Ni-Ti (called NiTiNOL), Ni-Al, Fe-Pt,
Cu-Al-Ni, Cu-Au-Zn, Cu-Zn-(Al,Ga,Sn,Si),
Ni-Mn-Ga 49
50. SMA
Common characteristics
Atomicordering transformation from
ordered parent phase to ordered martensite
phase
Thermoelastic martensitic transformation
that is crystallographic reversible
Martensite
phase that forms in a self-
accommodating manner (slip or twinning)
50
51. SMA
Typical plot of property changes versus temp.
A hysteresis is usually on the order of 20°C
51
52. One-way SMA
Sample is cooled from above Af to
below Mf → martensite forms
Sample has no shape change
Sample is deformed below Mf
Sample remains deformed
until heated.
Begin shape recovery at A and complete at A
s f
No shape change when cooled below Mf
Deforming the 52
martensite again will reactivate SME
53. Two-way SMA
Sample is cooled from above Af to
below Mf → martensite forms
Sample has no shape change
Sample is deformed below Mf
Sample remains deformed
until heated.
Begin shape recovery at A and complete at A
s f
Returnsto the deformed shape when cooled
below Mf 53